P is as efficient as Q and R together. Working together P and Q can complete a work in 18 days and R alone can complete it in 45 days. P and R work together for 12 days, Q alone complete the remaining work in:
Answer & explanation
Correct answer: option 2
Let total work = 90
Efficiency P + Q = \(\frac{90}{18}\) = 5 .......(i)
Efficiency of R = \(\frac{90}{45}\) = 2
ATQ,
P's efficiency = (Q + R)'s efficiency
P = Q + R
5 - Q = Q + 2 from (i)
2Q = 3 ⇒ Q = 1.5
So, P = Q + R = 1.5 + 2 = 3.5
Here,
Work done by P + R in 12 days = 12 × 5.5 = 66
Remaining work = 90 - 66 = 24
Remaining work done by Q in = \(\frac{24}{1.5}\) = 16 days